A numerical method for inverse design based on the inverse Euler equations

Recently, a fully coupled formulation of the surface shape design problem, called the direct design approach, has been proposed in which both the target surface pressure and the unknown nodal coordinates appear explicitly in the formulations. The proposed method is generally applicable, but in the past it has only been applied in the context of ideal fluid flows [Ashrafizadeh, A., , 505-527]. The present article extends the application of this method to the design of ducts carrying flows governed by the nonlinear coupled Euler equations, using a cell-centered finite volume method to discretize the governing equations. The details of the linearization and the imposition of the target pressure are discussed in this article. Also, the validation test cases and the design examples are presented, which show the robustness of the method in handling complex geometries and complex physical phenomena (such as shock waves). It is also shown that the computational cost of a direct shape design solution is comparable to the solution of the corresponding analysis problem.

Section: Introductionmentioning

confidence: 98%

A direct design approach using the Euler equations

Taiebi-Rahni

Ghadak

Ashrafizadeh

2008

“…In an inverse shape design problem, the shape of part of the boundary of the domain is unknown and target values for some field variables are prescribed instead. For example, airfoils can be designed to achieve a prescribed surface pressure distribution in an aerodynamic inverse shape design problem [2,3] or ducts can be designed to prevent pressure over-shoot and under-shoot and to minimize the head loss due to the flow separation in viscous flows [4,5].…”

Section: Introductionmentioning

confidence: 99%

A semi-coupled solution algorithm in aerodynamic inverse shape design

Ashrafizadeh

Okhovat

Pourbagian

et al. 2011

The numerical solution of an inverse airfoil design problem requires computational tools for grid generation, flow solution and the geometry update to provide the desirable shape corresponding to a given surface target pressure. Un-coupled as well as fully and semi-coupled shape design strategies have already been developed and employed. The target pressure is directly imposed in the fully coupled approach in contrast to un-coupled methods. Available semi-coupled methods use additional computational tools to couple the flow solver and the shape updater to directly impose the target pressure. In this article, a semicoupled numerical shape design strategy is introduced, in the context of an ideal flow model, in which the target tangential velocity is directly imposed while no additional computational tool is employed. Numerical test cases, implemented on both structured and unstructured grids, are carried out to compare the performance of the proposed method with an adjoint-based optimization technique. Results show that the semi-coupled method has a two to three times faster convergence rate as compared to the adjoint approach. However, the semicoupled solution convergence rate usually stalls after three orders of magnitude reduction of the objective function, while the un-coupled optimization method provides a more accurate solution. Therefore, a hybrid solution methodology is also advised, which provides faster convergence as well as lower computational errors as compared to both semi and un-coupled methods.

“…no flow separation and adverse pressure gradient control [5,6]). Approaches to the inverse problem solution are based on the potential flow theory and conformal mapping techniques, [4,7,8] on stream-function base formulations, [9][10][11] on boundary elements replacing the body surface [12] and on direct design methods. [13][14][15][16] Several examples of inverse problem solution methodologies are presented in [5,17] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A pseudo-compressibility method for solving inverse problems based on the 3D incompressible Euler equations

Ferlauto

2014

A numerical technique to solve the three-dimensional inverse problems that arise in aerodynamic design is presented. The approach, which is well established for compressible flows, is extended to the incompressible case via artificial compressibility preconditioning. The modified system of equations is integrated with a characteristic-based Godunov method. The solution of the inverse problem is given as the steady state of an ideal transient during which the flow field assesses itself to the boundary conditions, which are prescribed as design data, by changing the boundary contour. The main aspects of the Eulerian-Lagrangian numerical procedure are illustrated and the results are validated by comparing with theoretical solutions and experimental results.